This month's topics:

"We are in the midst of math all the time."

This from Dr. Kathy Mann Koepke of the National Institutes of Health. She's quoted by Lauran Neergaard, an Associated Press medical writer, in a March 26, 2013 AP release about the importance of very young children learning to understand how to use numbers to count and to measure. Neergaard also spoke with Dr. David Geary, who is leading an NIH-funded study of children's mathematical progress K-12. Geary terms this understanding "number system knowledge" (to be distinguished from the ability to estimate numbers without counting, which is innate in "young babies and a variety of animals.") As Neergaard explains it,

"What's involved? Understanding that numbers represent different quantities -- that three dots is the same as the numeral "3" or the word "three." Grasping magnitude -- that 23 is bigger than 17. Getting the concept that numbers can be broken into parts -- that 5 is the same as 2 and 3, or 4 and 1. Showing on a number line that the difference between 10 and 12 is the same as the difference between 20 and 22."

Children who lacked this fluency in first grade ended up in seventh grade lagging "behind their peers in a test of core math skills needed to function as adults," even correcting for IQ and attention span. "They're not catching up," according to Geary. And the defecits persist. Leergaard: "About 1 in 5 adults in the U.S. lacks the math competence expected of a middle-schooler, meaning they have trouble with those ordinary tasks and aren't qualified for many of today's jobs." As Mann Koepke puts it: "It's not just, can you do well in school? It's how well can you do in your life. We are in the midst of math all the time." Her advice to parents: integrate numbers meaningfully into what you say to your children, from the very beginning. Count things, measure things. This AP release was picked up by The Denver Post and USA Today.

Great Scientist $\neq$ Good at Math?

Without the question mark, this was the heading on an April 5 2013 Wall Street Journal piece by the eminent Harvard biologist E. O. Wilson, printed the next day in the paper. "During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail. This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent. It has created a hemorrhage of brain power we need to stanch." Wilson argues that

"exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition."

The math can be outsourced, later: "When something new is encountered, the follow-up steps usually require mathematical and statistical methods to move the analysis forward. If that step proves too technically difficult for the person who made the discovery, a mathematician or statistician can be added as a collaborator."

Starting with math is not a good idea: "The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail."

Wilson's dicta were sharply challenged by Edward Frenkel, the Berkeley Math Professor, in an April 9 posting on Slate, "Don't Listen to E.O. Wilson." Frenkel addresses Wilson's lament about bright students driven from science by their fear of math. "Turns out he actually believes not only that the fear is justified, but that most scientists don't need math. 'I got by, and so can you' is his attitude. Sadly, it's clear from the article that the reason Wilson makes these errors is that, based on his own limited experience, he does not understand what mathematics is and how it is used in science." Frenkel quotes Galileo ("The laws of Nature are written in the language of mathematics.") and explains the power of mathematics in organizing our perception of the world. He concludes: "It would be fine if Wilson restricted the article to his personal experience, a career path that is obsolete for a modern student of biology. We could then discuss the real question, which is how to improve our math education and to eradicate the fear of mathematics that he is talking about. Instead, trading on that fear, Wilson gives a misinformed advice to the next generation, and in particular to future scientists, to eschew mathematics. This is not just misguided and counterproductive; coming from a leading scientist like him, it is a disgrace." (See Frenkel's Multivariate Calculus lectures.)

"Mary, Queen of Maths"

On March 8, 2013, BBC News Magazine ran "A point of View: Mary, Queen of Maths," by Lisa Jardine (University College, London). The "Mary" is Mary Cartwright (1900-1998), an expert in differential equations, whose prominence in British science (elected to the Royal Society in 1947, President of the London Mathematical Society from 1961 to 1963, Dame Commander of the British Empire in 1969) was equaled by her personal modesty. Jardine quotes Freeman Dyson: "Only Cartwright understood the importance of her work as the foundation of chaos theory, and she is not a person who likes to blow her own trumpet." Dyson refers to work Cartwright did with J. E. Littlewood, starting in 1938. They investigated "a tricky type of equation," related to the then-secret development of radar: "Engineers working on the project were having difficulty with the erratic behaviour of high-frequency radio waves." As Dyson explains it: "The whole development of radar in World War Two depended on high power amplifiers, and it was a matter of life and death to have amplifiers that did what they were supposed to do. The soldiers were plagued with amplifiers that misbehaved, and blamed the manufacturers for their erratic behaviour. Cartwright and Littlewood discovered that the manufacturers were not to blame. The equation itself was to blame." Jardine tells us that this very early identification of chaotic behavior in a mathematical system went "largely overlooked for almost 20 years." But now: "The results unexpectedly obtained from the equations predicting the oscillations of radio waves are part of the foundation for the modern theory that accounts for the unpredictable behaviour of all manner of physical phenomena, from swinging pendulums and fluid flow, to the stock market."